Khan.scratchpad.disable(); For every level Ben completes in his favorite game, he earns $670$ points. Ben already has $430$ points in the game and wants to end up with at least $3900$ points before he goes to bed. What is the minimum number of complete levels that Ben needs to complete to reach his goal?
Answer: To solve this, let's set up an expression to show how many points Ben will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Ben wants to have at least $3900$ points before going to bed, we can set up an inequality. Number of points $\geq 3900$ Levels completed $\times$ Points per level $+$ Starting points $\geq 3900$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 670 + 430 \geq 3900$ $ x \cdot 670 \geq 3900 - 430 $ $ x \cdot 670 \geq 3470 $ $x \geq \dfrac{3470}{670} \approx 5.18$ Since Ben won't get points unless he completes the entire level, we round $5.18$ up to $6$ Ben must complete at least 6 levels.